Monotone Operators and the Proximal Point Algorithm

1976 ◽  
Vol 14 (5) ◽  
pp. 877-898 ◽  
Author(s):  
R. Tyrrell Rockafellar
Keyword(s):  
Proximal Point Algorithm ◽  
Monotone Operators ◽  
Proximal Point

scholarly journals An Approximate Proximal Point Algorithm for Maximal Monotone Inclusion Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Lingling Huang ◽  
Sanyang Liu ◽  
Weifeng Gao
Keyword(s):  
Hilbert Spaces ◽  
Proximal Point Algorithm ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Computational Results ◽  
Monotone Inclusion ◽  
Proximal Point ◽  
Inclusion Problems ◽  
Correction Step

This paper presents and analyzes a strongly convergent approximate proximal point algorithm for finding zeros of maximal monotone operators in Hilbert spaces. The proposed method combines the proximal subproblem with a more general correction step which takes advantage of more information on the existing iterations. As applications, convex programming problems and generalized variational inequalities are considered. Some preliminary computational results are reported.

A contraction proximal point algorithm with two monotone operators

2012 ◽  
Vol 75 (14) ◽  
pp. 5686-5692 ◽  
Author(s):  
Oganeditse A. Boikanyo ◽  
Gheorghe Moroşanu
Keyword(s):  
Proximal Point Algorithm ◽  
Monotone Operators ◽  
Proximal Point
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